VIBRATION WHEN ACCELERATING

My Maxima vibrates at random highway speeds. Mostly above 65 mph and always when accelerating above 55 mph. In many instances I will be driving on a level or downgrade and there will be no vibration at all which leads me to think I may have an axle or transmission problem as the vibration comes back when I step on the gas again. The vibration can get very bad shaking the entire car.